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Upper classes for the increments of the fractional Wiener process
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  • Published: December 1991

Upper classes for the increments of the fractional Wiener process

  • Karl Grill1 

Probability Theory and Related Fields volume 87, pages 411–416 (1991)Cite this article

Summary

LetX(t) be a fractional Wiener process, i.e., a centered Gaussian process on [0, ∞) with stationary increments and varianceEX 2 (t)=t 2α, anda(t) a positive nondecreasing function witha(t)≦t. We investigate the a.s. asymptotic behaviour of the incrementsI(t, a (t))=max{X{u+a(t))−X(u): 0≦u≦t−a(t)} (and some others that are similarly defined) ast→∞.

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References

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Authors and Affiliations

  1. Institut für Statistik und Wahrscheinlichkeitstheorie, TU Wien, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria

    Karl Grill

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  1. Karl Grill
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Cite this article

Grill, K. Upper classes for the increments of the fractional Wiener process. Probab. Th. Rel. Fields 87, 411–416 (1991). https://doi.org/10.1007/BF01304273

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  • Received: 11 April 1988

  • Revised: 25 April 1990

  • Issue Date: December 1991

  • DOI: https://doi.org/10.1007/BF01304273

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Keywords

  • Stochastic Process
  • Asymptotic Behaviour
  • Probability Theory
  • Mathematical Biology
  • Gaussian Process
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